The union of uniform closed balls conjecture

R. J. Stern

Concordia University, Montreal

ABSTRACT: For a closed set, the exterior sphere condition is compared

to proximal smoothness, and examples are provided which show that the

two properties are not necessarily equivalent. This clarifies a

semantic ambiguity occurring in the control theory literature. Then

conditions are given under which equivalence holds, and an open

question involving the union of uniform closed balls property is

stated in the form of a conjecture.